Metal interconnect modeling

ABSTRACT

A method for modeling metal routing includes extracting physical parameters of a metal interconnect for a circuit design, determining a resistance value from a database of metal interconnects with the extracted physical parameters, the resistance value being at a maximum frequency of a frequency range to be simulated, modeling the interconnect with a symmetric lumped transmission line model, and defining a resistance value of the lumped transmission line model to be about 1.05-1.3 times the resistance value taken from the database.

PRIORITY DATA

This patent is a non-provisional of U.S. Ser. No. 61/775,778 filed Mar.11, 2013, the entire disclosure of which is hereby incorporated byreference.

BACKGROUND

Integrated circuits that are formed into semiconductor substratesinclude multiple components such as transistors, resistors, and memoryelements. These components are typically connected to one anotherthrough metal lines that are routed through multiple layers formed ontothe substrate. These metal lines are often referred to as metalinterconnects.

During the design phase of integrated circuits, the designer often usesa computer drafting tool to design the circuit. The next step is todesign the layout of the circuit. The layout indicates how the circuitwill be printed onto a substrate. During this phase of the design, it isimportant to understand how each of the metal interconnects will performwhen carrying signals. It is particularly important to understand thebehavior of signals passing through the interconnects at a wide band offrequencies. For example, it may be useful to understand the behavior ofthe metal interconnects at a range between 0.2 Ghz and 60 Ghz. In somecases, even higher frequencies may wish to be analyzed.

Modeling or simulation software is often used to analyze the behavior ofmetal interconnects before they are printed out. This allows designersto make adjustments if some aspect of the circuit does not behave asdesired. Such modeling is often a time consuming and complicatedprocess. The equations that are used to model the metal interconnectsare relatively complex and thus take a lot of computing power.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects of the present disclosure are best understood from the followingdetailed description when read with the accompanying figures. It isemphasized that, in accordance with the standard practice in theindustry, various features are not drawn to scale. In fact, thedimensions of the various features may be arbitrarily increased orreduced for clarity of discussion.

FIG. 1 is a diagram showing an illustrative overview of a process formodeling metal interconnects, according to one example of principlesdescribed herein.

FIG. 2 is a diagram showing an illustrative lumped transmission linemodel with shielding, according to one example of principles describedherein.

FIG. 3 is a flowchart showing an illustrative method for setting valuesfor the lumped transmission line model with shielding, according to oneexample of principles described herein.

FIG. 4 is a diagram showing an illustrative lumped transmission linemodel without shielding, according to one example of principlesdescribed herein.

FIG. 5 is a flowchart showing an illustrative method for setting valuesfor the lumped transmission line model without shielding, according toone example of principles described herein.

FIG. 6 is a diagram showing a recursive skin effect model, according toone example of principles described herein.

FIG. 7 is a diagram showing an illustrative computer system that may beused to model metal interconnects, according to one example ofprinciples described herein.

FIG. 8 is a flowchart showing an illustrative method for modeling metalinterconnects, according to one example of principles described herein.

DETAILED DESCRIPTION

It is to be understood that the following disclosure provides manydifferent embodiments, or examples, for implementing different featuresof the disclosure. Specific examples of components and arrangements aredescribed below to simplify the present disclosure. These are, ofcourse, merely examples and are not intended to be limiting. Moreover,the performance of a first process before a second process in thedescription that follows may include embodiments in which the secondprocess is performed immediately after the first process, and may alsoinclude embodiments in which additional processes may be performedbetween the first and second processes. Various features may bearbitrarily drawn in different scales for the sake of simplicity andclarity. Furthermore, the formation of a first feature over or on asecond feature in the description that follows may include embodimentsin which the first and second features are formed in direct contact, andmay also include embodiments in which additional features may be formedbetween the first and second features, such that the first and secondfeatures may not be in direct contact.

Further, spatially relative terms, such as “beneath,” “below,” “lower,”“above,” “upper” and the like, may be used herein for ease ofdescription to describe one element or feature's relationship to anotherelement(s) or feature(s) as illustrated in the figures. The spatiallyrelative terms are intended to encompass different orientations of thedevice in use or operation in addition to the orientation depicted inthe figures. For example, if the device in the figures is turned over,elements described as being “below” or “beneath” other elements orfeatures would then be oriented “above” the other elements or features.Thus, the exemplary term “below” can encompass both an orientation ofabove and below. The apparatus may be otherwise oriented (rotated 90degrees or at other orientations) and the spatially relative descriptorsused herein may likewise be interpreted accordingly.

FIG. 1 is a diagram 100 showing an illustrative overview of a processfor modeling metal interconnects. According to certain illustrativeexamples, modeling often makes use of databases. For example, a numberof test structures 102 that include metal interconnects having variouslengths, widths, and metal schemes may be formed into a substrate. Theintrinsic characteristics of these varying interconnects are thenmeasured. Specifically, the resistance, capacitance, and inductance ofthese metal interconnects are measured and the data obtained from themeasurements are put into a measurement database 104. Moreover, thesemeasurements are obtained at varying frequencies.

The measurement database can be used to lookup the intrinsiccharacteristics of a specified metal interconnect. For example, aparticular metal interconnect may have the physical parameters of alength of X, a width of Y, and is placed within a metal scheme of typeZ. The database 104 may include intrinsic characteristics measured froma metal interconnect with parameters X, Y, and Z at varying frequencies.Thus, the measured capacitance, inductance, and resistance of that metalinterconnect may be obtained from the measurement database 104. In somecases, the exact physical parameters desired may not be within thedatabase 104. However, it may be that data from the database 104 isextrapolated to determine an approximate match for a metal interconnectwith the desired physical parameters.

As mentioned above, a circuit designer will use a computer drafting toolto create a circuit design 106. After designing the layout of thecircuit, an extraction tool 108 is used to extract the physicalparameters of the metal interconnects. The physical parameters are thencompared with measurements from the database 104 to determine values foruse in a lumped transmission line model 110. The lumped transmissionline model 110 may be of a variety of types of transmission linesincluding, but not limited to strip lines, microstrips, coplanarwaveguides, coplanar waveguides with shielding, interconnects betweendevices, and other waveguides.

A lumped transmission line model is a method for modeling a transmissionline using discrete components such as resistors, inductors andcapacitors to represent the intrinsic characteristics of thetransmission line. Various types of transmission line models may beused. According to examples described herein, a symmetric transmissionline model may be used as described in further detail below.

After using the database 104 and the physical parameters extracted fromthe circuit design 106 to define values for the lumped transmission linemodel, various adjustments 112 to those values may be made. According tocertain examples, these adjustments can be made to increase the accuracyof the lumped transmission line model 110. These adjustments will bedescribed in further detail below.

After the adjustments 112 have been made, various tools may be used tosimulate the circuit. For example, the circuit may be simulated usingS-parameters. S-parameters are a method for modeling circuits.Specifically, the electrical properties of a circuit such as gain,return loss, reflection coefficient and amplifier stability can beexpressed using S-parameters. By modeling and simulating metalinterconnects as described herein, the modeling and simulation can bedone more efficiently.

FIG. 2 is a diagram showing an illustrative symmetric lumpedtransmission line model 200 with shielding. Some substrates andsemiconductor devices include a layer of shielding that protects themetal interconnects from the intrinsic substrate effects. Specifically,the substrate will typically have a resistance and an inductance thataffects the characteristics of the metal interconnects. Because there isa shielding layer, those effects are not represented within the lumpedtransmission line model 200.

As illustrated, the interconnect is represented by a set of circuitcomponents between two ports 224, 226. The first half has a mainresistance 206 indicated by R1, a main inductance 208 indicated by L1and a main capacitance 210 indicated by C1. Likewise, the second halfhas a main resistance 216 indicated by R2, a main inductance 218indicated by L2 and a main capacitance 220 indicated by C2. C3 222indicates the combined capacitance of C1 and C2. The capacitance C3 222is primarily the capacitance resulting from the oxide layer formedbetween a metal layer and a semiconductor substrate.

The symmetric lumped transmission line model also factors in the skineffect. When alternating electric current flows through a conductor suchas a metal interconnect, the current distribution is not uniform throughthe conductor. Specifically, the electric current tends to be largertowards the edges of the conductor. Moreover, the skin effect changes asa function of frequency. For example, the resistance tends to becomegreater at higher frequencies. The skin effect is modeled by having askin resistance 202, indicated by Rs1, in series with a skin inductance204, indicated by Ls1. The series is in parallel with the mainresistance 206. The second half of the model also includes a skin effectas indicated by Ls2 214 and Rs2 212.

FIG. 3 is a flowchart showing an illustrative method for setting valuesfor the lumped transmission line model with shielding. As mentionedabove, the values for the components within the symmetric lumpedtransmission line model can be set in part by values obtained from thedatabase. The manner in which the values from the database can be usedto define values for the model 200 will now be described.

According to the present example, L1 and L2 are set to be of equalvalues. Moreover, L1 and L2 are set 302 so that the sum of L1 and L2 isequal to the inductance taken from the database at maximum frequency tobe simulated. For example, if the transmission line model is to simulatethe metal interconnect at a frequency range of 0.2 Ghz to 30 Ghz, thenthe maximum frequency is 30 Ghz. Specifically, a metal interconnect withsimilar physical parameters as extracted by the extraction tool is foundin the database. The database will also indicate an inductance value at30 Ghz. This is the value to which L1+L2 is set.

According to the present example, R1 is set 304 to the resistance takenfrom the database at the maximum frequency. Using the example of asimulation range between 0.2 Ghz and 30 Ghz, R1 is set to the resistanceof the metal interconnect from the database at 30 Ghz. Additionally, R2is set to be equal to R1.

According to the present example, Rs1 is set 306 so that Rs1 in parallelwith R1 is equal to the resistance taken from the database at theminimum frequency. Using the example of a simulation range between 0.2Ghz and 30 Ghz, Rs1 is set so that Rs1 in parallel with R1 is equal tothe resistance of the metal interconnect from the database at 0.2 Ghz.Those skilled in the relevant art are aware of the equations forcalculating resistances in parallel. Thus, a discussion of suchequations will not be given here.

According to the present example, Ls1 is calculated 308 using theresistance from the database at the center frequency to be simulated, inthis example, approximately 15 Ghz. Specifically, Ls1 may be calculatedusing the following equation, which indicates the real part only:[w ² *Ls1² *R1+(R1+Rs1)*R1*R11]/[(R1+Rs1)*(R1+Rs1)+w ² *Ls1² ]=R _(DAT)

Where:

R_(DAT)=the resistance from the database at center frequency; and

w=2*pi*(center frequency to be simulated);

Additionally, Rs2 is set to be equal to Rs1. Likewise, Ls2 is set to beequal to Ls1.

According to the present example, C3 is set 310 to be equal to one halfof the capacitance taken from the database at the minimum frequency.Additionally, C1 is equal to C2 and C1 plus C2 is equal to C3.

As mentioned above, certain adjustments are made to the model toincrease the efficiency and accuracy of the model. According to certainillustrative examples, R1 is increased by a factor within a range ofabout 1.05 to 1.3. R2 is likewise increased. For example, R1 and R2 canbe increased by approximately 10%. Doing so provides a better fit forthe transmission line model described herein with actual measuredresults.

FIG. 4 is a diagram showing an illustrative lumped transmission linemodel without shielding. As mentioned above, some metal interconnectsare unshielded and thus modeling of those interconnects should factor inthe substrate effects. Specifically, the substrate effects add asubstrate resistance 402 and a substrate capacitance 404. The remainingcomponents are similar to those described in FIG. 2.

FIG. 5 is a flowchart showing an illustrative method for setting valuesfor the lumped transmission line model without shielding. As mentionedabove, the values for the components within the symmetric lumpedtransmission line model can be set in part by values obtained from thedatabase. The manner in which the values from the database can be usedto define values for the model 200 will now be described.

According to the present example, L1 and L2 are set to be of equalvalues. Moreover, L1 and L2 are set 502 so that the sum of L1 and L2 isequal to the inductance taken from the database at the minimum frequencyto be simulated. For example, if the transmission line model is tosimulate the metal interconnect at a frequency range of 0.2 Ghz to 30Ghz, then the minimum frequency is 0.2 Ghz. Specifically, a metalinterconnect with similar physical parameters as extracted by theextraction tool is found in the database. The database will alsoindicate an inductance value at 0.2 Ghz. This is the value to whichL1+L2 is set.

According to the present example, R1 is set 304 to the resistance takenfrom the database at the maximum frequency. Using the example of asimulation range between 0.2 Ghz and 30 Ghz, R1 is set to the resistanceof the metal interconnect from the database at 30 Ghz. Additionally, R2is set to be equal to R1.

Like with the shielded method, Rs1 is set 506 so that Rs1 in parallelwith R1 is equal to the resistance taken from the database at minimumfrequency. Ls1 is also calculated 508 as described above. Moreover, likewith the shielded method, C3 is set 510 to ½ the capacitance from thedatabase at minimum frequency.

According to the present example the capacitance of the substrate, Csub,is set 512 so that C3 in parallel with Csub is equal to the capacitancetaken from the database at the maximum frequency. The substrateresistance, Rsub, is set 514 to be such that Rsub times Csub is equal toa defined value within a range from about 100 to 6000 ohm femtofarads,which may include the high resistive silicon substrate. Specifically,the value may be set at about 4000 ohm femtofarads. This value is basedon the intrinsic characteristics of standard substrate materials.Modeling the substrate effects in such a manner provides for efficiencywhile remaining accurate.

Again, R1 is increased by a factor within a range of about 1.05 to 1.3.R2 is likewise increased. For example, R1 and R2 can be increased byapproximately 10%. Doing so provides a better fit for the transmissionline model described herein with actual measured results.

FIG. 6 is a diagram showing a recursive skin effect model 600. Asmentioned above, the lumped transmission line model may account for skineffects by placing a skin resistance 202 in series with a skininductance 204, the series being in parallel with the main resistance206. To allow the model to be more accurate for higher frequencies, theskin effect may be modeled in a recursive manner.

Specifically, an additional skin resistance 602 may be placed in serieswith an additional skin inductance 604. This series is in parallel withthe original skin resistance 202. Modeling the skin resistance as suchmay allow for more accurate modeling up to 60 Ghz. The additional skineffect inductance 604 may be calculated using the equation describedabove. Except, the frequency used in the calculation is half of the sumof the minimum frequency to be simulated and the center frequency to besimulated. Additionally, Rs11 602, is set to the original value of Rs1202. Rs1 202 is then set to the resistance taken from the database atcenter frequency.

To further expand the bandwidth, this process of adding an additionalskin effect loop can be performed recursively. Specifically, a furtherskin effect resistance, Rs111 606 may be added in series with a furtherskin effect inductance, Ls111 608. This series is in parallel with theadditional skin effect resistance, Rs11 602. Rs111 and Ls111 may becalculated as described above for Rs11 and Ls11. Doing so may allow themodel to be more accurate for up to a bandwidth of 200 Ghz.

As mentioned above, after all of the components of the lumpedtransmission line model have been defined, the model can be simulatedover the desired frequency range. Various tools such as HSPICE, SPECTRE,and ELDO are available to perform such simulations. Such simulations maybe modeled using S-parameters. Using methods described herein ofconstructing the model and defining values for components within themodel, a quick and efficient method of modeling can be achieved.

FIG. 7 is a diagram showing an illustrative computer system that may beused to model metal interconnects. According to certain illustrativeexamples, the physical computing system 700 includes a memory 702 havingmodeling software 704 and data 706 stored thereon. The physicalcomputing system 700 also includes a processor 708 and a user interface710.

There are many types of memory available. Some types of memory, such assolid state drives, are designed for storage. These types of memorytypically have large storage volume but relatively slow performance.Other types of memory, such as those used for Random Access Memory(RAM), are optimized for speed and are often referred to as “workingmemory.” The various forms of memory may store information in the formof software 704 and data 706.

The physical computing system 700 also includes a processor 708 forexecuting the software 704 and using or updating the data 706 stored inmemory 702. In addition to storing the modeling software 704, the memory702 may store an operating system. An operating system allows otherapplications to interact properly with the hardware of the physicalcomputing system. The modeling software 704 may include the tools toform the lumped transmission line model and define the values of thecomponents therein.

A user interface 710 may provide a means for a user 712 to interact withthe system. The user may use various tools such as a keyboard or a mouseto input information into the physical computing system. Additionally,various output devices such as a monitor may be used to provideinformation to the user 712.

FIG. 8 is a flowchart showing an illustrative method for modeling metalinterconnects. According to certain illustrative examples, the methodincludes a step of extracting 802 physical parameters of a metalinterconnect for a circuit design. The method further includes a step ofdetermining 804 a resistance value from a database of metalinterconnects with the extracted physical parameters, the resistancevalue being at a maximum frequency of a frequency range to be simulated.The method further includes a step of modeling 806 the interconnect witha symmetric lumped transmission line model. The method further includesa step of defining 808 a main resistance value of the lumpedtransmission line model to be about 1.05-1.3 times the resistance valuetaken from the database.

According to certain illustrative examples, a method for modeling metalrouting includes extracting physical parameters of a metal interconnectfor a circuit design, determining a resistance value from a database ofmetal interconnects with the extracted physical parameters, theresistance value being at a maximum frequency of a frequency range to besimulated, modeling the interconnect with a symmetric lumpedtransmission line model, and defining a resistance value of the lumpedtransmission line model to be about 1.05-1.3 times the resistance valuetaken from the database.

According to certain illustrative examples, a computing system formodeling metal routing includes a processor and a memory. The memoryincludes computer readable instructions that when executed by theprocessor, cause the system to extract physical parameters of a metalinterconnect for a circuit design, compare the extracted physicalparameters for the interconnect with a database of measuredcharacteristics to determine a resistance value for the interconnect,the resistance value being at a maximum frequency of a frequency rangeto be simulated, model the interconnect with a symmetric lumpedtransmission line model, and define a resistance value of the lumpedtransmission line model to be the resistance value obtained from thedatabase multiplied by a factor within a range of about 1.05-1.3.

According to certain illustrative examples, a method for modeling metalrouting includes extracting physical parameters of a metal interconnectfor a circuit design, performing a comparison of the extracted physicalparameters for the metal interconnect with a database of measuredcharacteristics of metal interconnects of varying parameters at varyingfrequencies, defining a resistance value for a symmetric lumpedtransmission line model based on the comparison, adjusting theresistance value of the lumped transmission line model to be increasedby about 10 percent, and performing a simulation of the lumpedtransmission line model using s-parameters.

It is understood that various different combinations of the above-listedembodiments and steps can be used in various sequences or in parallel,and there is no particular step that is critical or required.Additionally, although the term “electrode” is used herein, it will berecognized that the term includes the concept of an “electrode contact.”Furthermore, features illustrated and discussed above with respect tosome embodiments can be combined with features illustrated and discussedabove with respect to other embodiments. Accordingly, all suchmodifications are intended to be included within the scope of thisinvention.

The foregoing has outlined features of several embodiments. Those ofordinary skill in the art should appreciate that they may readily usethe present disclosure as a basis for designing or modifying otherprocesses and structures for carrying out the same purposes and/orachieving the same advantages of the embodiments introduced herein.Those of ordinary skill in the art should also realize that suchequivalent constructions do not depart from the spirit and scope of thepresent disclosure, and that they may make various changes,substitutions and alterations herein without departing from the spiritand scope of the present disclosure.

What is claimed is:
 1. A method performed by a computing system formodeling metal routing in a circuit design, the method comprising:extracting physical parameters of a metal interconnect for the circuitdesign; determining a resistance value from a database of metalinterconnects with the extracted physical parameters, the resistancevalue being at a maximum frequency of a frequency range to be simulated;modeling the interconnect with a symmetric lumped transmission linemodel; defining an adjusted resistance value to be about 1.05-1.3 timesthe resistance value from the database; and simulating the symmetriclumped transmission line model across the frequency range using theadjusted resistance value as a main resistance value of the symmetriclumped transmission line model.
 2. The method of claim 1, whereinsimulating the symmetric lumped transmission line model comprises usingS-parameters.
 3. The method of claim 1, wherein the interconnect is ashielded interconnect.
 4. The method of claim 3, wherein a skininductance is defined by the inductance extracted from the physicalparameters at a frequency equal to half the sum of the minimum frequencyto be simulated and the center frequency to be simulated.
 5. The methodof claim 3, further comprising defining both inductances of thesymmetric lumped transmission line model as the inductance extractedfrom the physical parameters at a maximum frequency to be simulated. 6.The method of claim 1, wherein the interconnect is an unshieldedinterconnect.
 7. The method of claim 6, wherein the substrate resistanceand substrate capacitance for the lumped transmission line model aredefined such that a multiple of the substrate resistance and thesubstrate capacitance is within a range of about 100-6000 ohmfemtofarads.
 8. The method of claim 7, wherein the multiple is about4000 ohm femtofarads.
 9. The method of claim 6, further comprisingdefining both inductances of the symmetric lumped transmission linemodel as the inductance extracted from the physical parameters at aminimum frequency to be simulated.
 10. The method of claim 1, whereinthe adjusted resistance value is defined to be about 1.1 times theresistance value from the database.
 11. The method of claim 1, whereinthe transmission line model includes a skin effect model that comprisesa skin resistance and a skin inductance in series, the series being inparallel with the main resistance.
 12. The method of claim 11, whereinfor models that are to be simulated on a wider band, the skin effectmodel comprises an additional skin resistance in series with anadditional skin inductance, the series being in parallel to the skinresistance.
 13. The method of claim 12, in which the skin inductance isset based on a calculation using a frequency that is half of the sum ofthe minimum frequency to be simulated and the center frequency to besimulated.
 14. A computing system for modeling metal routing, the systemcomprising: a processor; and a memory including computer readableinstructions that when executed by the processor, cause the system to:extract physical parameters of a metal interconnect for a circuitdesign; compare the extracted physical parameters for the interconnectwith a database of measured characteristics to determine a resistancevalue for the interconnect, the resistance value being at a maximumfrequency of a frequency range to be simulated; model the interconnectwith a symmetric lumped transmission line model; define an adjustedresistance value to be the resistance value obtained from the databasemultiplied by a factor within a range of about 1.05-1.3; and simulatethe symmetric lumped transmission line model across the frequency rangeusing the adjusted resistance value as a main resistance value of thesymmetric lumped transmission line model.
 15. The system of claim 14,wherein the interconnect is a shielded interconnect.
 16. The system ofclaim 15, wherein a skin inductance is defined by the inductanceextracted from the physical parameters at a frequency equal to half thesum of the minimum frequency to be simulated and the center frequency tobe simulated.
 17. The system of claim 15, wherein the computer readableinstructions further cause the processor to define both inductances ofthe symmetric lumped transmission line model as the inductance extractedfrom the physical parameters at a maximum frequency to be simulated. 18.The system of claim 14, wherein the interconnect is an unshieldedinterconnect.
 19. The system of claim 18, wherein the substrateresistance and substrate capacitance for the lumped transmission linemodel are defined such that a multiple of the substrate resistance andthe substrate capacitance is within a range of about 100-6000 ohmfemtofarads.
 20. A method for modeling metal routing, the methodperformed by a computing system, the method comprising: extractingphysical parameters of a metal interconnect for a circuit design;performing a comparison of the extracted physical parameters for themetal interconnect with a database of measured characteristics of metalinterconnects of varying parameters at varying frequencies; defining aresistance value for a symmetric lumped transmission line model based onthe comparison; adjusting the resistance value of the lumpedtransmission line model to be increased by about 10 percent; simulatingthe lumped transmission line model using s-parameters; and the adjustedresistance value; and producing a circuit design based on thesimulation.